1. Field of the Invention
The present invention relates to digital imaging, and more particularly to a system and method treating noise in computed tomography (CT) projections and reconstructed images.
2. Discussion of Prior Art
Since it was first invented, computed tomography or CT has revolutionized the radiological fields in diagnosis, treatment/surgical planning, and follow-up evaluation of patient management. The fundamentals of the CT technology can be briefly depicted in two dimensions by FIG. 1A. The collected x-ray photons at detector bin i and projection angle θ is denoted by Iio(θ) in the absence of the body in the field-of-view (FOV) and by Ii(θ) in the presence of the body in the FOV, where notation x-y denotes the stationary coordinates and s-t denotes the rotating coordinates. The relation between Iio(θ) and Ii(θ) is given by the photon attenuation equation of
                                                        I              i                        ⁡                          (              θ              )                                =                                                    I                i                o                            ⁡                              (                θ                )                                      ⁢                          exp              ⁡                              [                                  -                                                            ∫                                              -                        ∞                                                                    +                        ∞                                                              ⁢                                                                  μ                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                    ⁢                                              ⅆ                        s                                                                                            ]                                                    ,                            (        1        )            where μ(x,y) represents the attenuation coefficient map of the body to be obtained 101.
As shown in blocks 102 and 103, by a mathematical manipulation of
                                                        p              i                        ⁡                          (              θ              )                                =                      ln            ⁡                          [                                                                    I                    i                    o                                    ⁡                                      (                    θ                    )                                                                                        I                    i                                    ⁡                                      (                    θ                    )                                                              ]                                      ,                            (        2        )            we have the well-known Radon transform of
                                          p            i                    ⁡                      (            θ            )                          =                              ∫                          -              ∞                                      +              ∞                                ⁢                                    μ              ⁡                              (                                  x                  ,                  y                                )                                      ⁢                                          ⅆ                s                            .                                                          (        3        )            
The attenuation coefficient map or CT image is reconstructed from the projection data {pi(θ)} over an angular sampling range of [0,π] by inverting the Radon transform of Eqn. (3) 104. The most widely used algorithm for the inversion is based on the filtered backprojection (FBP) technique.
Since the flux of x-ray photons toward the detector band are generated unevenly across the detector bins for i=1, 2, 3, . . . , (or laterally), due to the finite size of the tungsten target inside the x-ray tube, a system calibration is necessary on both the measurements of Iio(θ) and Ii(θ) for an artifact-free image reconstruction.
Currently available CT technology needs a very high x-ray photon flux or equivalently a high mA value (electric current across the x-ray tube) to generate a high quality diagnostic image. This translates into a high radiation exposure to the patient. Technically the need for a high mA value is partially due to the lack of an effective noise reduction technique on the measurement Ii(θ), since the measurement of Iio(θ) in the absence of the body does not have the dosage limitation and can be acquired with a very high mA value. Then the noise reduction task can be regarded as a task on Ii(θ).
Currently available spiral/helical CT technology have demonstrated the potential for dynamic imaging in four dimensions at less than 1 mm spatial resolution. However, as stated above, an important limitation for its clinical applications is associated with the high radiation exposure, especially for women and children. One solution is to deliver less x-rays to the body or equivalently lower down the mA value in data acquisition protocols. This will increase the image noise and make the diagnosis difficult.
Currently available spiral/helical CT technology needs a high output of x-ray flux from the x-ray tube to produce an adequate diagnostic image. This high x-ray flux is generated by a high electric current across the x-ray tube, reflected by a high mA protocol (of greater than 200 mA for most clinical studies). For a typical brain CT study, the associated radiation dosage is around the level of 3 Rads (a radiation dose unit), while the annual radiation exposure limit is around 5 Rads for the general population. Thus, two brain CT scans within a year would exceed the limitation. The associated radiation is an important limitation of CT clinical applications for massive screening of the vital organs, such as the heart, lungs, colon, and breasts. Most of the effort in reducing the radiation has been devoted to improving the hardware performance of CT scanners. Software approaches to reducing noise, and thus allowing for lower radiation, have had limited success.
Projection data acquired for image reconstruction of low-dose CT modality are degraded by many factors, including Poisson noise, logarithmic transformation of scaled measurements, and pre-reconstruction corrections for system calibration. All these factors complicate noise analysis on both the projection data and reconstructed images and render a challenging task for noise reduction in order to maintain the high image quality of currently available CT technologies. Up to now, various forms of filtering techniques have been developed to spatially smooth the projection data and/or the reconstructed CT images. One approach models the data noise by Gaussian distribution with variance proportionally depending on the signal or density of the data. It utilizes a nonlinear anisotropic diffusion filter to smooth the data noise. Another approach employs an adaptive trimmed mean filter to reduce streak artifacts, which are resulted from excessive x-ray photon noise in low-dose CT projections. Although both of them succeed in some degrees for noise reduction prior to image reconstruction, the assumption of the noise model is not justified in their applications. Furthermore, the filter parameters are based on ad hoc assumptions and lack of “ground truth.” Therefore, further development is then limited. Sauer and Liu [K. Sauer and B. Liu, Nonstationary filtering of transmission tomograms in high photon counting noise, IEEE Trans. Med. Imag. 10: 445–452, 1991] developed a non-stationary filtering method for the anisotropic artifacts in the image reconstruction. Although it utilizes local noise properties to construct a set of non-stationary filters, the method is a post-processing type approach on the images, and lacks “ground truth” basis. This type of filtering typically gains noise reduction at the cost of resolution.
Therefore, a need exists for a system and method of treating noise in low-dose CT projections and/or reconstructed images based on “ground truth” knowledge acquired from experimentation.